$C_\ell\wr S_n$的解列和欧拉差分表
Derangements and Euler's difference table for $C_\ell\wr S_n$
摘要：
与序列$\{n!\}$相关联的欧拉差分表自然地导出了无序排列的计数公式。本文研究了与序列$\{\ell^n n!\}$相关的欧拉差分表和广义排列问题。对于后表中出现的系数，我们将根据群$C_\ell\wr S_n$的两种$k$ -序列给出组合解释。特别是对于$\ell=1$，我们恢复了对称群的已知结果，而对于$\ell=2$，我们得到了超八面体群的相应结果。
英文摘要：
Euler's difference table associated to the sequence $\{n!\}$ leads naturally to the counting formula for the derangements. In this paper we study Euler's difference table associated to the sequence $\{\ell^n n!\}$ and the generalized derangement problem. For the coefficients appearing in the later table we will give the combinatorial interpretations in terms of two kinds of $k$-successions of the group $C_\ell\wr S_n$. In particular for $\ell=1$ we recover the known results for the symmetric groups while for $\ell=2$ we obtain the corresponding results for the hyperoctahedral groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
